The nonprofit medical organization said in a statement on Friday that there are now few places for those who need care in Khan Younis to go.
The Israeli army said on Tuesday that it had encircled Khan Younis, Gaza's second largest city, and was battling Hamas fighters. Israel intensified fighting this week and ordered the evacuation of everyone in certain neighborhoods, including the hospital.
Nasser Hospital is one of the main medical facilities operating in Khan Younis. Gaza's health ministry reported on Wednesday that no one was able to enter or exit because of bombardment.